Limiting distribution of periodic position measurements of a quantum harmonic oscillator

• DOI: 10.1016/j.physleta.2020.126397
• Publication Date: 2020-03-13T02:37:56Z
• Authors: Arnab Acharya; Debapriya Pal; Soumitro Banerjee; Ananda Dasgupta
• Keywords: Limiting; Position (finance); Harmonic; Quantum harmonic oscillator; Infinity

We consider a particle in harmonic oscillator potential, whose position is periodically measured with an instrument of finite precision. We show that the distribution of the measured positions tends to a limiting distribution when the number of measurements tends to infinity. We derive the expression for the limiting position distribution and validate it with numerical simulation.